Population Variation Reinforcement Worksheet

Name:

Date:

Statistical population variation illustration

📊 Part 1: Understanding Population and Variation

1. A researcher wants to study the average height of Year 11 students in New Zealand. Which of the following best describes the population?

All students at one Auckland school

All Year 11 students in New Zealand

100 randomly selected Year 11 students

All students in New Zealand

2. Which factors could contribute to variation in student test scores? (Select all that apply)

Study time

Prior knowledge

Test anxiety

Random chance

Teaching quality

3. The weights of kiwi birds in a sanctuary range from 1.2kg to 3.8kg. The variation in weight is most likely due to:

Measurement error only

Natural biological differences

All birds being identical

Poor data collection

4. A sample of 50 students from a population of 2000 shows test scores ranging from 45% to 95%. This demonstrates:

No variation exists

High variation in the sample

Low variation in the sample

Invalid data collection

✏️ Part 2: Applied Understanding

5. A café owner wants to determine the average amount customers spend. Define the population and suggest what might cause variation in spending amounts.

6. Complete the following statement: "In statistics, a _____________ is the entire group we want to study, while _____________ refers to the differences we observe between individual data points."

7. A researcher measures the daily temperature in Auckland for 30 days and finds temperatures ranging from 8°C to 22°C. Explain two different sources that could contribute to this variation.

8. Extension Challenge: A school has 800 students. Describe how you would select a representative sample of 80 students to study average study hours per week. What factors might cause variation in your results?

🎯 Success Criteria & Reflection

9. Self-Assessment: Check off what you can now confidently do:

Define what a population is in statistics

Identify sources of variation in data

Distinguish between natural variation and measurement error

Explain why variation is important in statistical analysis

10. Reflection: Write one real-world example where understanding population variation would be important for decision-making.

Teacher Notes:

Differentiation: Questions 1-4 focus on recognition, 5-7 on application, 8 provides extension. Students struggling with concepts should focus on questions 1-6. Advanced students should complete all questions and create their own population study scenario.